What Are the Solutions for e^z in Complex Numbers?

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    Complex Logarithm
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Homework Help Overview

The discussion revolves around solving equations involving the exponential function in the context of complex numbers, specifically the equations e^z = e and e^z = e^-z.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to solve the equations by guessing values for z and references a solution from the back of the book. Other participants question the understanding of the exponential function in complex form and suggest reviewing the calculation methods.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the exponential function in complex analysis. Some guidance has been offered regarding the calculation of e^(x + iy), but there is no explicit consensus on the solutions to the original equations.

Contextual Notes

The original poster expresses frustration with the textbook and indicates a lack of clarity on the topic, which may be affecting their understanding of the problem.

stihl29
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Homework Statement


e^z = e
e^z = e^-z


Homework Equations


they are the first 2 questions on my homework and my book is so bad i don't even know how to get the right answers, I've been online for over an hour I'm i'm sure they are easy.

The Attempt at a Solution


ffirst one just guessing ?
z = 1 ?
second in the back of the book says z = i*k*pi k = 1, 2, 3..
 
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What can you say about ex+iy for x and y real numbers?
 
e^x(cos(y) + isin(y)) = e??
i got that ones, i feel like I'm being really dumb and just not seeing something really simple
 
What? That doesn't make any sense. You should review how to calculate ex+iy by splitting it up into exeiy and calculating eiy
 

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